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DISTRIBUTION A: Presentation approved for public release. Distribution unlimited. Case Number 88ABW-2018-1258

Material Behavior Modeling

in the Aerospace Industry

Forging Industry

Technical Conference

11-12 September 2018

S.L. Semiatin

Air Force Research Laboratory

2DISTRIBUTION A: Presentation approved for public release. Distribution unlimited. Case Number 88ABW-2018-1258

Definitions and Motivation

• MODELING: Description of behavior of a material element during

processing (e.g., flow stress, microstructure/texture evolution, defect

evolution) or service (e.g., strength, creep, fatigue). Models can be

analytical or numerical. Models are usually one of two types:

phenomenological (curve fitting of observations…not readily

extrapolated) and mechanistic (based on metal physics)

• SIMULATION: The analysis of metal flow, phase change/

microstructure evolution, failure, etc. within a workpiece during

processing or service. Simulations are typically numerical (computer-

based) in nature for real-world problems.

• WHY DO WE DO MODELING AND SIMULATION: To predict important

material characteristics which are difficult or very expensive to

measure. Examples may include the internal microstructure,

formation of cavities, etc. For expensive aerospace materials with

often high buy-to-fly material-usage ratios and narrow processing

windows, modeling and simulation are indispensable to get it right

the first time!


Outline

• Some important aerospace alloys

• Flow stress models

• Microstructure evolution models

• Defect models

• Summary


Some Important (Two or More Phases) Aerospace Alloys

/ Titanium Alloys:

= hcp

= bcc

+ @ ~1825FForged conventionally

in + phase field

Cast + Wrought

Ni-Base Superalloys

g (fcc) grains

d Particles (for gs

control)

g, g precipitatesForged conventionally

in g+d phase field

Powder Metallurgy

Ni-Base Superalloys

g (fcc) grains (3-5 m)

g precipitates (0.02-2 m)Forged isothermally or conventionally in g+g

phase field

20 m

LSHR (~ME3, ME16)

50 m

Ti-6Al-4V

(at forging T)

5 m

Alloy 718

g

d


Outline



Why are they important

Phenomenolgical models and weaknesses

Temperature transient effects/mechanism models


• Defect models

• Summary


Why is Flow Stress Important

• Flow stress + friction + heat

transfer + die design affect press

load/needed press capacity.

• Flow stress affects die wear.

• Press-load variation during

forging run can provide indicator

of die wear.

• Key input for process simulations

like DEFORM


Phenomenological Flow Stress Models (e.g., Ti Alloys)

True Strain,

Tru

e S

tress,

• Often measured using isothermal hot compression tests at constant strain rates, .

• Data fitted to = C m at various levels of strain, , and put into look-up table.

• Weaknesses:

- Cannot be extrapolated beyond range of measurements.

- Cannot treat flow behavior for forging processes involving large temperature

transients, which are typical in conventional hot forging.

.

.

From: ASM Handbook, Vol. 22B, 2010.


Self-Consistent (SC) Model for Flow Stress (Ti-6Al-4V, Equiaxed- Microstructure)

0

50

100

150

200

250

300

800 850 900 950 1000

Temperature (oC)

Flo

w S

tre

ss

(M

Pa

)

Measurements - Semiatin

Measurements - Vandecastele

Measurements - Dajno & MontheilletSC Model (No texture effects)

Ti-6Al-4V: 0.1 s-1

Measurements - Semiatin and Bieler

Isothermal, 0.1 s-1

0

200

400

600

800

650 750 850 950

Temperature (oC)

Flo

w S

tres

s (

MP

a)

Nonisothermal DeformationSelf-Consistent Model

FEM 'Fit' (Shen, et al.)

0 s

1 s

= 1 s-1

.

Self-Consistent Model-

Isothermal Deformation

Non-isothermal, 1 s-1

• Used to estimate different strain rate in each phase;

instantaneous temperature from FEM simulation.

• Plastic flow of each phase described by its own flow curve.

• Rule of mixtures used to determine overall flow stress.

• For non-isothermal cases, concurrent microstructure

evolution (i.e., phase fractions) simulated using diffusion

model which incorporates temperature transient.


0

10

20

30

40

50

0 0.5 1 1.5 2

Tru

e S

tress (

MP

a)

True Strain

10-3 s-1

10-4 s-1

775C 815C

Ultrafine Ti64

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Tru

e S

tre

ss

(M

Pa)

True Strain

1065C

1135C

True Strain

Tru

e S

tress (

MP

a)

5

25

20

15

10

0 0.10

0.2 0.3 0.4 0.5 0.6 0.7

PM Ni-Base Superalloy (LSHR)

0.0005 s-1

Flow Behavior during Low-Strain-Rate Isothermal Forging/Superplastic Forming

Increase in flow stress with strain

(flow hardening) due to increase in

grain/particle size (i.e., coarsening),

not strain hardening.

Generalized Constitutive Eqn

Description of Coarsening

3r 3or = Kd (t to)

)()( p

2r

bn

G

σ)

kT

ADGb(ε =

. p


Flow Behavior during Quenching (After Heat Treatment)

Non-uniform cooling of large workpieces after

heat treatment produces small and non-

uniform plastic strains that give rise to bulk

residual stresses Need descriptions of flow

behavior under appropriate strain, strain rate,

and temperature conditions.

-6.5 -6 -5.5 -5 -4.5 -4

Log Plastic Strain Rate (s-1)

2.2

2.4

Lo

g S

tress (

MP

a)

2.0

m = 0.16

m = 0.36

PM Superalloy (LSHR)

980C

“On-Cooling” Stress-Relaxation TestSolution treat at a high temp, cool to test temp,

prestrain, then relax flow stress vs strain rate

AFRL Concurrent Cooling/Straining TestSolution treat at a high temp, cool and plastic strain

at constant rates flow stress vs temperature at a

constant plastic strain rate

Tru

e S

tress (

MP

a)

Temperature (K)

0

200

400

600

Temperature (K)

200

400

1150 1250 1350 1450

153 K/min

1.13 x 10-4 s-1

Stress-

Relaxation Data

600


Outline





Phenomenological modeling

Mechanistic modeling

• Defect models

• Summary


Why are They Important

• Microstructure is sensitive to

forging process variables and

is often important in setting

processing windows.

• For a given alloy, there are a

wide range of microstructures,

each with its own suite of

service properties.

• Microstructure can be difficult

to discern via NDE techniques.

• Crystallographic texture leads

to directionality in properties.

• Microstructural and textural

defects can cause rejection of

forgings.


Some Microstructural Irregularities

1000 m

200 m

Cast + Wrought Superalloys

25 mm

Abnormal

Grain

Ti-6Al-4V

/ processing (ingot

to billet; part forging)

Microtexture (aka

macrozones)

/ hot working

(forging, rolling,

etc) + annealing

abnormal grain

growth

ALA (‘as large as’)

unrecrystallized

grains in billets,

forgings


Phenomenological Models:Recrystallization & Phase Transformation

Avrami/JMAK Equation

X = 1 – exp(-ktn)X: fraction recrystallized

or transformedk: rate constantt: time (or strain)

n: Avrami exponent

StrengthsEasy to useEasy to couple with FEM results

LimitationsApplicable only for specific alloy for

which measurements were fittedDifficult to apply for situations

involving variable temperature, strain rate, etc

Provides only spatial averages

Waspaloy

From: G. Shen, et al., Metall. Mater. Trans. A, 1995, vol. 26A, p.1795.

DYNAMIC RECRYSTALLIZED FRACTION

n = 3, T<1010C

n = 2, 1010C<T<1027C

n = 1.8, 1027C<T


Meso (Grain) Scale Mechanism-Based Models

Monte Carlo (Potts) and Cellular Automaton Models – Recrystallization & Grain Growth

From: O.M. Ivasishin,, et al., Mater. Sci. Eng. A, 2006, vol. A433, p.216.

Advanced Mesoscale Models for Recrystallization and Grain Growth

PSN

Source: J.P. Thomas

Recrystallized Fraction during Cogging


Meso (Grain) Scale Mechanism-Based Models (Cont’d)

Nucleation, Growth, and

Coarsening of Precipitates

100nm

0.8

1.2

1.6

2

2.4

0 1 2 3

Lo

g [

gs

Dia

(n

m)]

Log [Cooling Rate (K/s)]

AC CubeOQ CubeWQ Cube

Model Predictions using Deff for A

Strain-Free Mat’l

Slope ~ -0.5

Datum from Induction/

Gleeble HT Experiments

(C/s)

Models for Texture Formation (Deformation,

Transformation, Recrystallization)

Measured

Predicted

Z

Z

From: M.G. Glavicic, et al., Metall. Mater. Trans. A,

2008, vol. 39A, p. 887.


Outline




• Defect models


Phenomenological modeling: Cavitation & fracture

Mechanistic modeling: Cavitation

• Summary


Why are Defect Models Important

• Defects lower product yield.

• Internal defects may be

difficult/expensive to detect by NDE

methods and lead to greatly-reduced

service properties (e.g., fatigue

resistance).

• Validated models can reduce trial-

and-error fixes to eliminate defects.

Source: Ladish Co.


Cavity Observation: Ti-6Al-4V with a Colony- Microstructure

50 m

5 m

50 mm


• Criterion based on experimentally-measured damage

factor C*:

C* = (t / ) d (= work done by max tensile stress through the

effective strain)

t maximum tensile stress

effective stress

effective strain

• Original use of C+L criterion: Fracture occurs at critical

damage level Cf*. (Useful for surface fracture prediction.)

• C + L extension: Cavity “initiation” occurs at critical

damage level Ci* ; i.e., initiation said to occur when

cavities can be found at 500X magnification. (Useful for

predicting formation of internal cavities.)

_

_

_ _

Cockroft + Latham (C+L) Phenomenological Model: Cavitation & Fracture for Complex States of Stress


C+L Criterion: Ti-6Al-4V with a Colony- Microstructure

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5 10 15

C*

Ci*

Distance from Free Surface (mm)

Dam

ag

e P

ara

mete

r

ForgingI.D.

HeightRed. (%)

255063.575

f

815C

• Measured depth of cavities: 3.5 mm (25 pct.

reduction), 10.75 mm (50 pct. reduction)

• Free-surface fracture observations: two small free-

surface cracks (50 pct. reduction), many surface

cracks (63.5 pct. reduction)

2 mm

Ci* and Cf* from cavitation

observations during hot

tension testing

Hot Pancake Forging

Comparison of C

values from FEM

simulations and

critical values for

cavity initiation (Ci*)

and fracture (Cf*)

from tension tests.


Equiaxed (/ Processed)Colony ( Processed )

From: V. Venkatesh and S.P. Fox, Microstructural Modeling and

Prediction during TMP, TMS, 2001, p. 147 .

Microstructure Dependence of Ci* for Initiation of Internal Cavities: Ti-6Al-4V


Cavitation Model: Hot Working of Ti-6Al-4V with a Colony Structure

Size of Largest Cavities

in Pancake ForgingPlasticity-Controlled

Cavity-Growth Model

From: P.D. Nicolaou, S.L. Semiatin, Metall. Mater. Trans. A, 2005, vol. 36A, p. 1567 .


Summary

• A variety of phenomenological- and mechanism-based models exist to

predict the effect of forging variables on flow stress, microstructure

evolution, and defect formation for aerospace alloys.

• Phenomenological models are essentially curve fits to experimental

data and are thus useful primarily for the specific temperature/ strain-

rate regime used to make the measurements. Thus, the extrapolation

of such results can introduce substantial errors in forging process

simulating.

• Mechanism-based models are useful in providing more detailed

information such as the effect of temperature and strain rate

transients during hot working on plastic flow and microstructure

evolution, including detailed spatial variations. Such models often rely

on accurate input material data. In a number of cases, mechanism-

based models can be coupled to process-simulation codes (e.g.,

DEFORM) and thus be used for forging process design.

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